INF 223, Spring 2008, Plan of Lectures


This semester I will rearrange the course towards applications in (object-oriented) modeling and Model Driven Architecture. In the first part I will give an introduction into Category Theory based on Part 1 of the following book of Jose Fiadeiro Categories for Software Engineering In the second, applied part I will discuss the formalization of (diagrammatic) specification techniques like UML class diagrams, ER diagrams, database schemata, XML, ... I plan to close the course with an outline of a theory of model transformations based on this formalization. Articles and/or handouts, covering the second part will be made available during the course.






Nr.DateWeekTopicsPages





1.21.01.08 4- What is Category Theory?
- outline of the course
VII - XII, 1 - 11
2.23.01.08 4- graphs and graph homomorphisms with examples
- opposite graphs
15 - 20





28.01.08 5 no lecture (cordination problems) 20 - 22
3.30.01.08 5- path in a graph
- definition of a category with examples: SET, GRAPH
- category of paths of a graph
20 - 22





4.04.02.08 6- category LOGI and general pre-orders as categories
- category MULT of sets and multi-functions
- diagrams and commutative diagrams
23 - 27
5.06.02.08 6 - isomorphisms with examples: SET, GRAPH, LOGI
- isomorphic objects have the same "social life"
- monomorphisms
27 - 29





6.11.02.08 7 - epimorphisms
- split monomorphisms and split epimorphisms
- opposite category
- duality principle
- subcategories, full subcategories and discrete categories
29 - 32
7.13.02.08 7 - discussion of "typing"
- slice categories
- initial objects with example in SET
33 - 38, 58





8.18.02.08 8 - initial and terminal objects
- examples in SET, LOGI, MULT
- definition of sum with example in SET, LOGI and for power sets
58 - 65
9.20.02.08 8 - sums in slice categories
- definition of product with example in SET, LOGI and for inheritance
- definition of pushouts and pushouts in SET
- equivalence relations and quotient sets
65 - 70





10.25.02.08 9 - pushouts in SET
- pushouts by sums and co-equalizers
- actualization/instantiation as pushout
70 - 75
11.27.02.08 9 - equalizers and pullbacks
- general construction and examples of pullbacks
- specializations of pullback and pushout constructions





12.03.03.0810 - co-cones and colimits
- cones and limits
- completeness and co-completeness
75 - 81
13.05.03.0810 - stepwise construction of limits and colimits
- diagrams as functors
- functors with examples
- category CAT





14.10.03.0811 - examples and definition of free functors
15.12.03.0811 - natural transformations
- adjoint functors





17.03.0812 no lecture (conference)
19.03.0812 no lecture (conference)





24.03.0813 Easter Monday
27.03.0813 no lecture (conference)





31.03.0814 no lecture (conference)
02.04.0814 no lecture (conference)





16.07.04.0815
17.09.04.0815





18.14.04.0816
19.16.04.0816





20.21.04.0817
21.23.04.0817





22.28.04.0818
23.30.04.0818 - course overview





05.05.0819 no more lectures










22/23 Oral Exam